Asynchronous Algorithmic Alignment with Cocycles

Andrew Joseph Dudzik, Tamara von Glehn, Razvan Pascanu, Petar Veličković

Keywords: algorithmic reasoning, graph neural networks, category theory, bellman-ford, commutative monoids, idempotence, cocycles, monoid homomorphisms, dynamic programming

TL;DR: Target algorithms we would like (G)NNs to execute are often highly asynchronous. We show how to build synchronous GNNs that are provably invariant under forms of asynchronous computation.

Abstract: State-of-the-art neural algorithmic reasoners make use of message passing in graph neural networks (GNNs). But typical GNNs blur the distinction between the definition and invocation of the message function, forcing a node to send messages to its neighbours at every layer, synchronously. When applying GNNs to learn to execute dynamic programming algorithms, however, on most steps only a handful of the nodes would have meaningful updates to send. One, hence, runs the risk of inefficiencies by sending too much irrelevant data across the graph. But more importantly, many intermediate GNN steps have to learn the identity functions, which is a non-trivial learning problem. In this work, we explicitly separate the concepts of node state update and message function invocation. With this separation, we obtain a mathematical formulation that allows us to reason about asynchronous computation in both algorithms and neural networks. Our analysis yields several practical implementations of synchronous scalable GNN layers that are provably invariant under various forms of asynchrony.

Submission Type: Full paper proceedings track submission (max 9 main pages).

Submission Number: 141